Problem: Simplify the following expression: $ z = \dfrac{-1}{10} - \dfrac{1}{7p - 1} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7p - 1}{7p - 1}$ $ \dfrac{-1}{10} \times \dfrac{7p - 1}{7p - 1} = \dfrac{-7p + 1}{70p - 10} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{1}{7p - 1} \times \dfrac{10}{10} = \dfrac{10}{70p - 10} $ Therefore $ z = \dfrac{-7p + 1}{70p - 10} - \dfrac{10}{70p - 10} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-7p + 1 - 10 }{70p - 10} $ Distribute the negative sign: $z = \dfrac{-7p + 1 - 10}{70p - 10}$ $z = \dfrac{-7p - 9}{70p - 10}$